Practice Degree Of Vertices In Cartesian Product (4.5.2)

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6 sample questions

Question 1.
Define the Cartesian product of two graphs.
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Think about ordered pairs and pairs of vertices.
Question 2.
What is the degree of a vertex?
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Count the connections!
3Question 3.
What is the degree of vertex (u,v) in the Cartesian product?
- deg(u) + deg(v)
- deg(u) * deg(v)
- deg(u) - deg(v)
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Think about how the degrees interact together.
4Question 4.
If a graph G has no edges, what is the degree of all vertices?
- True
- False
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Remember degrees count edges!
Question 5.
Consider two graphs A and B where A has 3 vertices with degrees [0, 1, 2] and B has 3 vertices with degrees [1, 1, 1]. Calculate the degrees in the Cartesian Product.
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Assess every pair in the product using the summed degrees.
Question 6.
Given two graphs C and D, where C has a vertex of degree 4 and D with a vertex of degree 0, discuss the implications on the product graph's connectivity.
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Consider how degree zero affects the overall performance in connectivity.

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